04. 15 Supply chain network design under uncertainty- A comprehensive review and future research directions

European Journal of Operational Research 263 (2017) 108–141 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor Production, Manufacturing and Logistics Supply chain network design under uncertainty: A comprehensive review and future research directions Kannan Govindan a,∗, Mohammad Fattahi b, Esmaeil Keyvanshokooh c a Center for Sustainable Supply Chain Engineering, Department of Technology and Innovation, University of Southern Denmark, Campusvej 55, Odense, Denmark b School of Industrial Engineering and Management, Shahrood University of Technology, Shahrood, Iran c Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI 48109, USA a r t i c l e i n f o Article history: Received 16 October 2015 Accepted April 2017 Available online April 2017 Keywords: Supply chain management Supply chain network design Uncertainty Stochastic programming Risk consideration Robust optimization a b s t r a c t Supply chain network design (SCND) is one of the most crucial planning problems in supply chain management (SCM) Nowadays, design decisions should be viable enough to function well under complex and uncertain business environments for many years or decades Therefore, it is essential to make these decisions in the presence of uncertainty, as over the last two decades, a large number of relevant publications have emphasized its importance The aim of this paper is to provide a comprehensive review of studies in the fields of SCND and reverse logistics network design under uncertainty The paper is organized in two main parts to investigate the basic features of these studies In the first part, planning decisions, network structure, paradigms and aspects related to SCM are discussed In the second part, existing optimization techniques for dealing with uncertainty such as recourse-based stochastic programming, risk-averse stochastic programming, robust optimization, and fuzzy mathematical programming are explored in terms of mathematical modeling and solution approaches Finally, the drawbacks and missing aspects of the related literature are highlighted and a list of potential issues for future research directions is recommended © 2017 The Authors Published by Elsevier B.V This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Contents ∗ Introduction Scope and review methodology Decision-making environments for SCND under uncertainty SCM issues in designing SC networks 4.1 Network structure and uncertain parameters 4.2 Planning horizon and decisions for SCND 4.3 Risk management in SCND problem 4.4 Resilient SCND 4.5 Different paradigms in SCM 4.5.1 Responsive SCND 4.5.2 Green SCND 4.5.3 Sustainable SCND 4.6 Humanitarian SCND 4.7 Other SC characteristics Optimization under uncertainty for SCND 5.1 Optimization criteria for evaluation of SC networks’ performance Corresponding author E-mail addresses: kgov@iti.sdu.dk (K Govindan), mohammadfattahy@shahroodut.ac.ir (M Fattahi), keyvan@umich.edu (E Keyvanshokooh) http://dx.doi.org/10.1016/j.ejor.2017.04.009 0377-2217/© 2017 The Authors Published by Elsevier B.V This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) 109 110 110 112 112 114 115 116 116 116 116 117 117 117 117 117 K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 5.2 5.3 5.4 SCND problems with continuous stochastic parameters Chance-constrained programming for SCND Scenario-based stochastic programs for SCND 5.4.1 Two-stage stochastic programs 5.4.2 Multi-stage stochastic programs 5.4.3 Scenario generation for stochastic SCND problems 5.5 Risk measures in the context of SCND 5.6 Robust optimization in the context of SCND 5.6.1 Robust models with discrete scenarios 5.6.2 Robust models with interval-uncertainty 5.7 Fuzzy mathematical programming in the context of SCND 5.8 Optimization approaches for SCND with disruptions Applications and real-word case studies for SCND Discussion, conclusions, and future research directions 7.1 SCM aspects in SCND under uncertainty 7.2 Optimization aspects in SCND under uncertainty Acknowledgment Appendix A Features and structure of logistics networks in the related literature Appendix B Mathematical definition of well-known risk measures in the related literature References Introduction In the early 1980s, SCM was introduced in order to respond to fierce competition among companies (Oliver & Webber, 1982) Over time, a growing number of corporations realized the significance of integrating their operations into key supply chain (SC) processes instead of managing them separately, thus extending the SCM evolution (La Londe, 1997) As pointed out by Handfield and Nichols (1999), SCM is "The holistic management approach for integrating and coordinating the material, information and financial flows along a supply chain." In accordance with SimchiLevi, Kaminsky, and Simchi-Levi (2004) and the Council of Supply Chain Management Professionals, Melo, Nickel, and Saldanha-DaGama (2009) also defined SCM to be "The process of planning, implementing and controlling the operations of the supply chain in an efficient way." Several issues, such as appearance of short-life products, fierce competitions in today’s markets, increasing expectations and changing customers’ preferences, the development of new technologies, and globalization have led business enterprises to make large investments in their SCs (Simchi-Levi et al., 2004) A SC, a complex network of organizations and facilities which are mostly settled in a vast geographical area or even the globe, synchronizes a series of interrelated activities through the network (Christopher, 1999) The SC network is also referred to as the logistics network by Simchi-Levi et al (2004), and Ghiani, Laporte, and Musmanno (2004) defines the SC as "a complex logistics system in which raw materials are converted into finished products and then distributed to final users (consumers or companies)." On the other hand, Hugos (2011) points out that some differences exist between logistics management and SCM In essence, logistics management, as a portion of SCM, focuses on activities such as inventory management, distribution, and procurement that are usually made on the boundaries of a single organization, while SCM includes other activities such as marketing, customer service, and finance as well SCND, also called strategic supply chain planning, is a part of the planning process in SCM, which determines the infrastructure and physical structure of a SC Over the last two decades, SCND has been considered as a suitable application for facility location (FL) models Revelle, Eiselt, and Daskin (2008) characterized existing FL models into four main types: continuous, network, analytic, and discrete In spite of many differences among these models, they all include a set of customers with known locations and a set of facilities whose locations should be specified Most SCND models belong to the category of discrete location models (Melo et al., 2009) 109 118 119 119 119 121 124 125 125 126 126 127 128 130 130 130 132 132 133 137 137 Several review papers exist on FL models, (e.g., Daskin, 2011; Owen & Daskin, 1998) and some surveys focus particularly on discrete location models (e.g., Klose & Drexl, 2005; Mirchandani & Francis, 1990; Revelle et al., 2008) However, FL models in the context of SCM have been reviewed by only a few papers, including Daskin, Snyder, and Berger (2005), Shen (2007b), and Melo et al (2009) Therefore, there is still ample room to survey SCND models and methods Large investments are usually required to make strategic decisions in SCND These decisions are very difficult to change and have long-term effects on SC’s performance The most common strategic decisions consist of determining locations and number of facilities, capacities and sizes of facilities, technology and area allocation for production and process of products at different facilities, selection of suppliers, and so on (Simchi-Levi et al., 2004) Over time (generally between three and five years), when a company has been influenced by these decisions, many parameters, including demand, capacity, and costs of its SC network, can have major fluctuations Further, the parameters associated with SCND involve an enormous volume of data, often resulting in wrong estimations due to inaccurate forecasts and/or poor measurements in the modeling process (e.g., aggregation of demand points and products) Thus, SCND under uncertainty has obtained significant attention in both practice and academia over recent years Designing reverse logistics (RL) networks is another type of optimization problem based on the FL models The RL networks are often designed for the purpose of collecting used, refurbished, or defective products from customers and then carrying out some recovery activities Due to the stringent pressures from environmental regulations, many companies have been confronted with the challenge of designing RL networks Locating facilities to perform recovery activities is one of the key strategic decisions to be made in this problem Indeed, these facilities should operate properly over many years under uncertain business environments Thus, the task of dealing with existing uncertainty in the return quantities and other parameters of RL networks plays a significant role in designing them RL network design under uncertainty has attracted a great deal of attention and, as a result, an investigation into this problem is included in our review paper as well It is noteworthy that this problem has many similarities to the SCND in terms of optimization approaches Further, the forward and reverse logistics networks are often integrated, also known as closed-loop supply chain (CLSC) network 110 K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 The main purpose of this paper is to review the studies and optimization approaches developed for designing SC, CLSC, and RL networks under uncertainty Briefly, our major research questions in this field are: i Which SCM paradigms and issues are addressed? ii What sources of uncertainty are considered? iii How are uncertain parameters modeled and integrated into the existing mathematical formulations? iv Which optimization techniques and tools are mostly utilized? v Which real-world case studies are investigated? In this regard, Snyder (2006) represented a survey on stochastic and robust FL problems without consideration of SCM aspects Reliable FL models for SCND with disruptions were studied by Snyder and Daskin (2007) Furthermore, a critical review on optimization models for robust design of SC networks was represented by Klibi, Martel, and Guitouni (2010) They categorized existing uncertainties in the SCND problem and investigated their impacts on the network as well Moreover, SCND has been the subject of many recent review papers focusing on other SC features (e.g., Farahani, Rezapour, Drezner, & Fallah, 2014; Eskandarpour, Dejax, Miemczyk, & Péton, 2015) However, to the best of our knowledge, there has not been any review paper in the area of SC and RL network design under uncertainty that focused on both SCM aspects and optimization techniques Therefore, in the presented survey on this area:  A comprehensive and categorized review is provided in accordance with network structure, planning decisions and main SCM issues  Various uncertainty sources and different uncertainty modeling approaches for developing an optimization model are studied  Optimization techniques, including modeling and solution approaches to deal with uncertainty, are investigated as a general framework  Relevant real-life applications and case studies are explored  Finally, significant research gaps are introduced to be investigated as future studies by scholars and researchers The remainder of this paper is organized as follows: In Section 2, the scope and our research procedure are introduced In Section 3, different related decision-making environments are discussed The associated papers are categorized consistent with the SCM issues in Section Optimization aspects in the related literature are investigated in Section The studies addressing real-world applications are introduced in Section Finally, in Section 7, a discussion, conclusions and possible future research directions are explicated OR recovery network OR distribution network) AND (design OR planning) AND (stochastic OR uncertain OR robust OR risk OR fuzzy OR reliable OR resilient), we obtained 259 journal papers from Scopus However, many of them were not published in ISI indexed journals or more specifically, they did not satisfy the second or third criteria, which are the key considerations in this study Further, the scope of this survey was addressed with other keywords such as transportation–production, and transportation–inventory networks by a few studies in the past Therefore, to resolve the limitations of our search keywords and provide a comprehensive review, we have completed our survey by utilizing other survey and review papers in the area of SCND, FL, and SCM Using all afore-mentioned search strategies, 170 journal papers, published from 20 0 up to now, are explored We refer to them as reference papers from now on The distribution of these reference papers in terms of their publication date is shown in Fig In Fig 1, more than 50% of these papers were published from 2012 up to now where many developments and much progress have been made in the area of optimization, and this recent trend reveals the importance of uncertainty in the area of SCND problem In addition, Fig elucidates the share of international journals that have the highest contributions in publishing the reference papers: European Journal of Operational Research and Transportation Research Part E: Logistics and Transportation Review occupy first and second rank by publishing 17 and 15 papers, respectively Additionally, Table displays existing review papers in the relevant literature Note that all these papers are in the area of SCM, but some of them explored the FL or logistics network design models in SCM, specifically Their scope and special features are reported in Table Moreover, the numbers of reference papers that have some overlapping with our review paper are put in the last column of Table As shown by Table 1, while there are overlapping areas between other review papers and ours, to our knowledge, no review paper has examined the aspects taken into account in this paper In summary, the purpose of this paper is to explore the studies that have been made in the area of SCND (including CLSC and RL network design as well) under uncertainty to highlight the research gaps and future research directions Therefore, the reference papers are investigated in terms of different uncertain decisionmaking environments, network structures, planning decisions, various paradigms and aspects of SCM Further, we examine different optimization approaches to deal with uncertainty in these studies The papers that have addressed a SC of a real-life case study or specific industry are also discussed Scope and review methodology Decision-making environments for SCND under uncertainty In this paper, peer-reviewed articles published over the last two decades in ISI indexed journals in the context of SCND (including RL and CLSC network design as well) under uncertainty are studied We consider three criteria for these papers, including: (1) the paper must be written in English; (2) one of the decision variables is location or selection of facilities from potential candidates for at least one layer of SC; and finally, (3) at least one of the problem’s parameters is uncertain Published papers in international journals among electronic bibliographical sources including Scopus and Web of Science have been searched by using a combination of different keywords Firstly, we searched on 12 June 2015 by using keywords (supply chain network design OR strategic supply chain planning) AND (stochastic OR uncertain OR robust OR risk OR fuzzy OR reliable OR resilient), and we came up with 33 and 24 journal papers from Scopus and Web of Science, respectively Then, using wider combinations of keywords, (Supply chain OR logistic OR supply network Several parameters of a SCND problem, such as costs, demand, and supply, have inherent uncertainty Moreover, SC networks can be affected by major man-made or natural disruptions such as floods, terrorist attacks, earthquakes, and economic crises However, these kinds of disruptions usually have a low likelihood of occurrence, but their impacts on SC network are prominent The objective of SCND under uncertainty is to achieve a configuration so that it can perform well under any possible realization of uncertain parameters But, this measure of performing well for different SC networks under uncertain environments could be quite different according to the viewpoints of decision makers Based on the definition of different decision-making environments by Rosenhead, Elton, and Gupta (1972) and Sahinidis (2004), uncertain environments for the SCND problem can be categorized according to the following groups: K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 111 Fig Publication date distribution of reference papers Fig Share of international journals with the highest contributions in publishing the reference papers Table Scope and special features of relevant review papers Articles Facility location/ logistics network design focus Scope and special features Akỗal, ầetinkaya, and Üster (2009) Melo et al (2009) Klibi et al (2010) × × × Elbounjimi, Abdulnour, and Ait-KadiI (2014) Farahani et al (2014) Eskandarpour et al (2015) Heckmann et al (2015) Govindan, Soleimani, and Kannan (2015) × × × Network design for Reverse and Closed loop supply chains Facility location models in the context of SCM Optimization approaches, key random environmental factors and disruptive events in SCND under uncertainty Green closed loop supply chain network design Competitive SCND Sustainable SCND Supply chain risk Reverse logistics and Closed loop supply chains Group (G1): Decision-making environments with random parameters in which their probability distributions are known for the decision maker Here, these parameters are called stochastic parameters Stochastic parameters in SCND are described by either continuous or discrete scenarios In a smaller part of Group 1, the stochastic parameters are described using a known continuous probability distribution This type of SCND problem – except for simple networks with one location layer – engenders intractable optimization models Additionally, the customers’ demand is the most popular stochastic parameter in these studies, which is modeled through the normal distribution with known mean and variance A discussion about these studies is provided in Section 5.2 Sheppard (1974) was one of the seminal authors who used a scenario approach for a FL problem; gradually, this approach has been exploited for SCND The scenario approach leads to tractable optimization models By this approach, we can describe various stochastic parameters having different probability distributions with consideration of dependency among them Therefore, this approach is quite common for describing stochastic parameters (Snyder, 2006) A complete review of this group of uncertain decision-making environments is provided in Section 5.4 Number of shared reference papers 16 26 16 Group (G2): Decision-making environments with random parameters in which the decision maker has no information about their probability distributions Under this setting, robust optimization models are usually developed for SCND with the purpose of optimizing the worst-case performance of SC network The random parameters in this decision-making group are divided into either continuous or discrete To model discrete uncertain parameters, the scenario approach has been used However, for continuous uncertain parameters, some pre-specified intervals are defined This approach is also called interval-uncertainty modeling Optimization models for SCND under this group of decision-making environments are studied in detail in Section 5.6 Group (G3): Fuzzy decision-making environments In general, there exist two types of uncertainties including ambiguity and vagueness under the fuzzy decision-making environment Ambiguity denotes the conditions in which the choice among multiple alternatives is undetermined However, vagueness states the situations in which sharp and precise boundaries for some domains of interest are not delineated In this context, fuzzy mathematical programming handles the planner’s expectations about the level of objective function, the uncertainty range of coefficients, and the satisfaction level of constraints by using membership functions 112 K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 Fig Frequency of reference papers with respect to different uncertain decision-making environments (see Inuiguchi & Ramık, 20 0; Sahinidis, 20 04) The studies belonging to this group are discussed in Section 5.7 Fig presents the frequency of reference papers according to the above-mentioned uncertain decision-making environments SCM issues in designing SC networks In this section, the relevant papers are categorized based on the main aspects of SCM including the structure of network, decision variables, and SCM’s paradigms 4.1 Network structure and uncertain parameters A SC network converts raw materials into final products and then delivers them to customers It includes various types of facilities, and each type plays a specific task in the network A set of facilities with the same task and type is called a layer or echelon A crucial aspect of SCND studies is the number and type of layers and the layers in which location decisions are determined The usual layers of SC networks are composed of suppliers, plants, distribution centers, warehouses, and customers and the typical material flows are often from suppliers to customers It is noteworthy that another issue driven by real-life applications is the necessity to deal with multi-product problems Regarding the material and product flows in a SC network, some studies have the assumption of being single-sourcing, which means a facility or a customer can be served by only one facility from its upstream layer (e.g., Georgiadis, Tsiakis, Longinidis, & Sofioglou, 2011; Shen & Daskin, 2005) Moreover, some studies have regarded the material/product flows in one layer of SC, called intra-layer flows (e.g., Aghezzaf, 2005; Mousazadeh, Torabi, & Zahiri, 2015) Furthermore, direct flows from upper layers to customers have been taken into account in the literature (e.g., Govindan, Jafarian, & Nourbakhsh, 2015; Vila, Martel, & Beauregard, 2007) In Fig 4, different types of these material flows for a typical SC network are shown In this paper, the studies related to RL network design under uncertainty are also reviewed Several studies in the relevant literature have focused on designing only a RL network (also called a recovery network) and some others have integrated forward and reverse networks, named a CLSC network As stated by Melo et al (2009), the strategic planning for RL networks has many similarities with forward logistics networks The main differences are the type of facilities they use and the direction of flows In RL networks, the reverse flows are often started by collecting used and defective products from customers and their final destination is usually recovery, remanufacturing, disposal centers, or secondary markets (Keyvanshokooh, Fattahi, Seyed-Hosseini, & Tavakkoli-Moghaddam, 2013) Table Defined abbreviations for uncertain parameters Uncertain parameter Abbreviation Demand Cost of activities (e.g., transportation, production) Capacity of network facilities/ transportation links Supply quantity for network facilities Required capacity for producing products Capacity coefficients for holding products/materials in SC facilities Parameters of demand distribution function Selling price of finished products Buying price of raw materials Conversion rates of materials/components/products to process other materials/components/products in network facilities Safety-stock levels for products in SC facilities Processing/production time for network facilities Transportation time through entities of SC network Supply time for network facilities Fuzzy goals to represent aspiration levels of multiple objectives Availability of network facilities Availability of transportation links/modes between network’s entities Disrupted products/supply/commodities in SC facilities Return quantities in a RL or CLSC network Disposal rate of returns in a RL or CLSC network Buying price of returns in a RL or CLSC network Proportion of returned products/components for different activities (e.g., remanufacturing, recycling, refurbishing) in a RL or CLSC network Profit of recycling/remanufacturing returned products in RL or CLSC network Selling price of RL outputs (products/components/raw materials) to customers in a RL or CLSC network Demand for RL outputs (products/components/raw materials) in a RL or CLSC network Financial parameters such as tax, exchange, and interest rate Environmental parameters such as environmental impacts of SC’s activities and facilities Social parameters related to designing logistics networks D C CA S CR CS DP P PR CP SS PT TT ST FG AF AT DC R DR BP PA PP SP DS FP EP PS Another important feature of SCND problem is that it is sometimes assumed that there is a primary structure for a SC network and then the goal is to redesign it (e.g., Aghezzaf, 2005) The most uncertain parameters that have been assumed in designing logistics networks in the reference papers are listed in Table Here, we present some abbreviations for these parameters, which are used in the following sections of the paper In Appendix A, the reference papers are characterized based on the structure of the forward SC network in Table A.1 CLSC and RL network design models are categorized according to the structure of RL network in Table A.2 The uncertain parameters and their classification on the basis of different decision-making environments are also illustrated in Tables A.1 and A.2 In these tables, we assign numbers to the reference papers, which have been utilized in the following sections to analyze them K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 113 Fig A SC network structure with different types of product flows Fig Frequency of uncertain parameters in the forward logistics network of reference papers Fig Frequency of uncertain parameters in the RL network of reference papers By analyzing tables in Appendix A, we highlight many key facts about logistics network design models under uncertainty One of the most significant factors is the frequency of uncertain parameters assumed in designing forward and RL networks, which is illustrated by Figs and 6, respectively In Table 3, the forward SC and CLSC network design models are categorized according to the forward network structure and the type of decision-making environment under uncertainty Table represents this classification for the reverse and CLSC network design models based on the RL network features Here, the network features include the number of commodity and the number of layers in which location decisions are specified This idea of classification has been gained from Melo et al (2009) From Tables to 4, we can conclude that most reference papers have considered single or two location layers A few papers have dealt with RL or CLSC network design problem under uncertainty and about 70% of them have explored SCND problem without consideration of RL activities In optimization problems under uncertainty, decision-making environments depend on available information for uncertain parameters and their source of uncertainty Klibi et al (2010) investigated different existing uncertainties in SC as well as their sources and impacts Here, G1 and G2 have the highest and lowest frequencies among the reference papers’ decision-making environments, respectively Moreover, a few papers have assumed combined uncertain decision-making environments to model their SC network on the basis of type and features of their uncertain parameters (e.g., Keyvanshokooh, Ryan, & Kabir, 2016; Sadghiani, Torabi, & Sahebjamnia, 2015; Torabi, Namdar, Hatefi, & Jolai, 2016; Vahdani, Tavakkoli-Moghaddam, Modarres, & Baboli, 2012) Among the reference papers, about 19% of them have addressed SCND problem with disruption The influences of disruptions on 114 K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 Table Classification of SC and CLSC network design models based on the decision-making environment and features of forward logistics network location layer location layers location layers >3 location layers Single commodity Multiple commodities Single commodity Multiple commodities Single commodity Multiple commodities Single commodity Multiple commodities G1 G2 G3 [3,4,5,8,9,10,11,13,15,18,19,20,21,22,23,24,29,33,34,42,44,45,50, 54,55,57,61,62,63,67,70,72,73,75,86,87,88,90,96, 100,101,104,105,107,112,113,121,122,130,143] [6,17,25,28,35,38,51,68,69,71,78,80,84,89,99,108, 124,139,144,145,153] [36,40,46,74,85,114,115,118,120,126,127,137,149,150,156] [1,2,7,12,26,32,37,43,47,48,52,56,58,59,60,64,91,93,95,98, 109,125,136,159] [106,155] [14,16,30,39,76,97,111,132,134,157] [66] [53,81,128] [79,152,154] [99,138,139,153] [133,137,146,156] [92,159] [27,77,82,94,110,146,149,150,151] [31,65,116,123,131] [141,148,157] [41,103] [140,142] [49] [129] [158] Table Classification of RL and CLSC network design models based on the decision-making environment and features of RL network G1 location layer location layers location layers >3 location layers Single commodity Multiple commodities Single commodity Multiple commodities Single commodity Multiple commodities Single commodity Multiple commodities [23,70,162,164] [25,38,83] [85,156, 161,165] [26, 28,47,84,91,99,102,139,147,168] [40,137, 149, 150] [97,169, 170] G2 G3 [79, 83,148, 160] [156] [92,154] [137,146, 166] [81,128,135,163] [65,83,167] [110] [99,102,123,138, 139] [53, 119,146,149,150,151] [117] [129,134] the physical structure of a SC network may result in having uncertainty in some parameters Facilities’ capacity, availability of facilities and their connections, and amount of disrupted products in SC facilities are the most frequent parameters, which have been assumed uncertain because of disruption events It must be noted that disruptions can deeply fluctuate costs, demand and supply parameters, which should be of more interest to future researchers 4.2 Planning horizon and decisions for SCND Due to the complexity of SC networks in today’s business environment, it is important to consider several planning decisions along with the classical location-allocation decisions to achieve an integrated system These planning decisions remain constant for different time spans and may be divided into three categories, including strategic (long-term), tactical (mid-term), and operational (short-term) level decisions according to their time spans In the strategic level, there are usually several crucial SC decisions to be made such as the number, locations, and capacity of facilities While it depends entirely on the nature of the SC, strategic decisions typically hold for about three to five years Tactical decisions are usually made for three months to three years and operational decisions (e.g., vehicle routing decisions) are often constant for one hour to one trimester (Vidal & Goetschalckx, 1997) It should be noted that holding these decisions for a certain time span is mostly dependent on the nature of SC and thus it can vary for different SCs Fig illustrates different SC decisions (except locationallocation, production, and inventory decisions that are considered in the majority of the related literature), which have been determined in SCND problems As shown by Fig 7, the decisions associated with different planning levels are taken into account in the related literature However, several decisions such as products’ price and routing decisions have been addressed by a few studies Pricing decisions are usually put at the tactical planning level and routing decisions be- long to the operational planning level, which are rarely integrated with SCND under uncertainty in the related literature Distribution networks, often the ending part of a SC network, consist of products flows from depots to customers or retailers The design of such network requires solving two hard combinatorial optimization problems including determining the depots’ locations and vehicle routes to serve customers For the first time, Salhi and Rand (1989) revealed numerically that solving the FL and routing problems separately leads to suboptimal solutions Then, the location-routing problem gained substantial attention Recently, Prodhon and Prins (2014) presented a survey paper in this area In the context of SCND under uncertainty, Ahmadi-Javid and Seddighi (2013), Javid and Azad (2010), and Azad and Davoudpour (2013) addressed the FL and routing decisions simultaneously under uncertainty In the majority part of literature, the decisions have been made for a single period As explained by Melo et al (2009), these singleperiod SCND models may be enough to obtain a robust configuration for a network and also a robust set of operational and tactical decisions Moreover, another part of the literature has addressed SCND problem with a planning horizon including multiple periods In these studies, the periods can be divided into (1) tactical/operational time periods, or (2) strategic time periods In the studies with multiple tactical or operational periods (e.g., Schütz, Tomasgard, & Ahmed, 2009; Tsiakis, Shah, & Pantelides, 2001), strategic decisions are made at the beginning of planning horizon while tactical or operational decisions, such as products allocation to customers and inventory levels, are able to be changed in different periods throughout the planning horizon In addition, some studies consider the possibility of applying future adjustments in the SC strategic decisions These kinds of adjustments are typically made for location and/or capacity of facilities, for example, due to unstable condition of target markets, expansion opportunities for new markets, and budget limitations for investments Thus, a planning horizon divided into several strategic periods is assumed (e.g., Aghezzaf, 2005; Nickel, Saldanha-daGama, & Ziegler, 2012) K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 115 Fig Main planning decisions (except location-allocation, production, and inventory) in the reference papers cilities can be closed, opened, or reopened more than once over a planning horizon Further, expanding, reducing, or relocating facilities’ capacities are another key issue Melo, Nickel, and Da Gama (2006) investigated different approaches to make capacity planning for a deterministic dynamic FL problem However, the papers that addressed these concerns in multi-period SCND problem under uncertainty are still scarce It is worth mentioning that a limited number of studies in deterministic SCND problems (e.g., Correia & Melo, 2016; Fattahi, Mahootchi, & Husseini, 2016; Fattahi, Mahootchi, Govindan, & Husseini, 2015; Salema, Barbosa-Povoa, & Novais, 2010) have used a planning horizon including interconnected strategic and tactical periods, but no study has yet regarded this issue under an uncertain environment 4.3 Risk management in SCND problem Fig Frequency of reference papers in terms of their planning horizon Fig classifies the SCND models under uncertainty that considered a planning horizon with multiple strategic periods or multiple tactical/operational periods It also compares the frequency of single-period SCND models with multiple-periods ones It can be drawn from Fig that most SCND models under uncertainty are single-period There exist some practical features related to SCND problems with multiple strategic periods Sometimes, it is presumed that fa- Risk management in SCM has gained considerable attention in both practice and academia recently Unfortunately, there is not a clear and comprehensive consensus for definition of supply chain risk Sodhi, Son, and Tang (2012) explored researchers’ perspectives in this area and emphasized that their perspectives are widely diverse Moreover, Heckmann, Comes, and Nickel (2015) asserted that no unique definition has been provided for the SC risk Further, the term risk is still a rather vague concept and generally, risk comprehension is based on the fear of losing (business) value Heckmann et al (2015), after examining various relevant research works, defined the supply chain risk as the potential loss for a SC in terms of its objectives caused by uncertain variations in SC features due to occurrence of triggering-events Further, they provided some major characteristics of SC risk that one can refer to this study for more details In SCND problem under uncertainty, consistent with a presented classification by Tang (2006a), SC risks can be divided into operational and disruption risks based on the source of uncertainties As pointed out by Behdani (2013) and Snyder, Atan, Peng, 116 K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 Table Reference papers dealing with operational or disruption risks in SCND problem under uncertainty Reference papers Share (%) 14% Operational risks Azad and Davoudpour (2013), Azaron, Brown, Tarim, and Modarres (2008), Baghalian et al (2013), Franca et al (2010), Gebreslassie, Yao, and You (2012), Goh et al (2007), Guillén et al (2005), Guillén, Mele, Bagajewicz, Espuña, and Puigjaner (2003), Huang and Goetschalckx (2014), Jabbarzadeh et al (2014), Jin et al (2014), Kara and Onut (2010b), Kazemzadeh and Hu (2013), Madadi, Kurz, Taaffe, Sharp, and Mason (2014), Nickel et al (2012), Pan and Nagi (2010), Pasandideh, Niaki, and Asadi (2015), Ramezani, Bashiri, and Tavakkoli-Moghaddam (2013a), Sabio, Gadalla, Guillén-Gosálbez, and Jiménez (2010), Sadghiani et al (2015), Soleimani and Govindan (2014), Soleimani, Seyyed-Esfahani, and Kannan (2014), and Govindan and Fattahi (2017) Disruption risks Jabbarzadeh, Naini, S., Davoudpour, and Azad (2012), Mak and Shen (2012), Ahmadi-Javid and Seddighi (2013), Azad et al (2014), Baghalian 5% et al (2013), Jabbarzadeh et al (2014), Klibi and Martel (2012a), Klibi and Martel (2013), Noyan (2012), and Sadghiani et al (2015) Rong, Schmitt, and Sinsoysal (2016), supply chain disruption is an event that may occur in a part of SC due to natural disasters (e.g., earthquakes and floods) or through intentional/unintentional human actions (e.g., war and terrorist attacks), which have undesired effects on SC’s goal and performance Moreover, the operational risks are rooted in intrinsic uncertainties of SC, such as uncertainty in supply, demand, lead-time, transportation times and costs This risk type usually has no influence on functionality of SC’s elements, while it affects the operational factors, which are basically assumed to be uncertain However, the disruption risks evoked by SC disruptions can affect functionality of SC’s elements either completely or partially for uncertain time duration In Table 5, the studies that dealt with risk management (either operational or disruption risk) in the context of SCND problem under uncertainty are classified In most studies in Table 5, risk measures have been utilized in an optimization problem to cope with the existing risk We discuss these risk measures in detail in Section 5.5 4.4 Resilient SCND It is crucial to regard SC disruptions while designing a SC network since there are a few recourses for making strategic decisions when a disruption happens However, firms can adjust their tactical and operational decisions under disruptions Planning for SC networks with disruptions was studied by Snyder, Scaparra, Daskin, and Church (2006) in terms of mathematical modeling This issue is discussed on Section 5.8 For a SC under uncertainty, there exist a number of strategies that can be utilized to manage the risk associated with disruptions In accordance with Tomlin (2006), mitigation strategies are those where a SC takes some preventive actions in advance of a disruption and also pays their related costs regardless of whether a disruption takes place, while contingency strategies are those where a SC takes several actions merely when a disruption happens with the aim of returning SC to its original condition As pointed out by Christopher and Peck (2004) and Tang (2006a), resilience is a system or firm’s capability to return to its initial condition or even to a more desirable state after disruption In SCM, this ability is directly affected by SC resources and design of its network Indeed, a resilient supply chain network should operate efficiently both normally and in the face of a disruption Regarding resilient SCND under disruption events, a few papers employed mitigation strategies These strategies are discussed in detail on Section 5.8 Measuring the resiliency of SCs is still a questionable task and different resilience indicators have been defined in the existing literature In this regard, Cardoso, Barbosa-Póvoa, Relvas, and Novais (2015) investigated the performance of different resilience metrics and indicators for various types of SC networks and Spiegler, Naim, and Wikner (2012) presented an assessment framework of resilience In fact, the choice of approaches for designing resilient SC networks is contingent upon many factors such as availability of financial resources, network structure, risk preference of decision maker, and so on 4.5 Different paradigms in SCM In a SC, the initial goals include meeting demand of customers, functionality of SC’s processes, and accessibility of SC’s resources (Heckmann et al., 2015) SCND was seeking traditionally to achieve these goals economically However, the business goals of a company affect its SCND problem and, in fact, a suitable design of SC network enables the company to attain its goals and competitive advantages If a corporation wants to become successful in today’s market, both its SC and competitive strategies should fit together to have aligned goals Over the last decade, various paradigms have been proposed in SCM that influence designing a SC network In this section, we explore these paradigms briefly 4.5.1 Responsive SCND Besides economic goals, several companies consider responsiveness of their SC as another goal to attain competitive advantages Different definitions exist for the SC responsiveness: the ability of a SC to produce innovative products, meet short lead-times, cope with a wide range of products, and meet a high service level (Chopra & Meindl, 2013) Gunasekaran, Lai, and Cheng (2008) defined the SC responsiveness as a paradigm that has emerged in response to the volatile and competitive business environment; thus, a responsive SC has to be highly flexible to changes of market or customer requirements In a optimization problem for designing responsive SC networks, several studies considered objective functions such as minimizing service time of customers (e.g., Cardona-Valdés, Álvarez, & Ozdemir, 2011; Mirakhorli, 2014; You & Grossmann, 2011), maximizing fill rate of customers’ demands (e.g., Shen & Daskin, 2005), and minimizing lateness of products’ delivery to customers (e.g., Pishvaee & Torabi, 2010) Fig represents the studies that dealt with responsive SCND models under uncertainty Recently, Fattahi, Govindan, and Keyvanshokooh (2017) presented a stochastic model for designing responsive and resilient supply chain networks with delivery lead-time sensitive customers 4.5.2 Green SCND The increasing importance of environmental issues for SCs has resulted in integrating different environmental factors in SCND models instead of only focusing on pure economic models This integration can be applied as either environmental measures in objective functions or environmental constraints in the mathematical model Green SCND is another paradigm that aims to merge economic and environmental goals/factors in designing SC networks Fig specifies studies that regarded environmental concerns It is worth noting that the effects of SC activities on the environment have been considered as uncertain parameters in Guillén-Gosálbez and Grossmann (2010), Guillén-Gosálbez and Grossmann (2009), Pishvaee, Razmi, and Torabi (2014), Pishvaee, Torabi, and Razmi (2012), and Babazadeh, Razmi, Pishvaee, and Rabbani (2017) Furthermore, mitigating the environmental disruptions via wastes of used products is another significant environmental issue K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 117 Fig Classification of different paradigms in SCND problem under uncertainty (Farahani et al., 2014) In this regard, many researchers (see studies in Table A.2 of Appendix A) have studied designing RL networks for recovery of used products 4.5.3 Sustainable SCND A definition for sustainable development was made by the World Commission on Environment and Development (WCED) as "a development that satisfies present needs without compromising the capability of future generations to meet their own resources and needs" (Brundtland, 1987) As mentioned by Farahani et al (2014), sustainable SCs play an essential role in conserving natural resources for the next generation and gaining the attention of many researchers over recent years Based on this paradigm, several scholars have tried to design SC networks consistent with economic aspects, environmental performance, and social responsibility that are called sustainable SCND (Eskandarpour, et al., 2015) We have identified that the majority of studies in this area presumed a deterministic decision-making environment such as Mota, Gomes, Carvalho, and Barbosa-Povoa (2015) and You, Tao, Graziano, and Snyder (2012) Recently, Eskandarpour et al (2015) have presented a survey on sustainable SCND and investigated existing approaches for assessment of the environmental impact and social responsibility performance of SCs In Fig 9, the reference papers based on the above-mentioned paradigms are categorized It should be noted that in Fig 9, the studies that have considered environmental issues directly in their constraints or objective function(s) are reported and we not report all studies related to RL and CLSC From Fig 9, a small percentage of papers (about 19%) have addressed the responsiveness goals, environmental performance or social responsibility Further, Pishvaee et al (2014) and Dayhim, Jafari, and Mazurek (2014) among the reference papers of our study regarded the social responsibility and environmental performance concurrently for designing a sustainable SC network under uncertainty 4.6 Humanitarian SCND Studies in SCND are not limited only to business SCs Nonbusiness SCs such as public and governmental ones have been much attracted over recent years (e.g., Jabbarzadeh, Fahimnia, & Seuring, 2014; Jeong, Hong, & Xie, 2014; Liu & Guo, 2014; Noyan, 2012) A humanitarian SC, also called relief SC, often designed to alleviate suffering of vulnerable people in the event of a disaster or even after that, is one of the most popular non-business SCs As pointed out by Najafi, Eshghi, and Dullaert (2013), a disaster is an event that often leads to destruction, damage, human suffering, loss of human life, and/or deterioration of health service Humanitarian logistics network design is usually placed in the category of pre-disaster planning; naturally, it is under uncertainty associated with the impact of different types and magnitude of disasters (Özdamar & Ertem, 2015) It should be noted that optimization approaches for pre-disaster FL are reviewed by Caunhye, Nie, and Pokharel (2012) 4.7 Other SC characteristics In this section, two important issues regarding SCND problem are briefly discussed It should be emphasized that these presented facets have not been widely investigated in the related context Financial factors: There are a limited number of papers in the area of SCND under uncertainty in which financial factors are taken into account International financial factors have strong impact on the structure of global SCs and several studies, such as Goh, Lim, and Meng (2007) and Hasani, Zegordi, and Nikbakhsh (2015), dealt with this issue As the second category, a few studies such as Longinidis and Georgiadis (2013) and Longinidis and Georgiadis (2011) assumed that the financial cycle of a corporation is also affected by the operations related to its SC; hence, they presented financial operation constraints to model the financial cycle In the last category, budget constraints are embedded into SCND problem to limit investment on designing SCs In this regard, Nickel et al (2012) considered budget constraints for designing a SC under stochastic demand and interest rates They also presumed that there are different alternative investment options and thereby imposing a target for the return on investment Moreover, there are a few reference papers in which financial parameters such as tax, exchange, and interest rates are assumed to be uncertain These studies include Goh et al (2007), Nickel et al (2012), and Longinidis and Georgiadis (2013) Competition: Recently, Farahani et al (2014) presented a survey paper on competitive SCND In general, the competitive environments for designing a SC network can be categorized into three primary groups: (1) competition among facilities in the same echelon of SC, (2) competition among facilities in different echelons of SC, and (3) competition among multiple SCs However, the uncertain models that addressed FL under a competitive environment are presented only in the context of pure FL, so this area has a high potential for future research directions Optimization under uncertainty for SCND In this section, optimization aspects of the related literature are investigated in separate subsections Moreover, the reference papers belonging to Groups 1, 2, and (based on the definitions in Section 3) are studied in terms of mathematical modeling, solution methods, and optimization techniques 5.1 Optimization criteria for evaluation of SC networks’ performance To design a SC network under uncertainty, single or multiple objectives are often considered for a numerical optimization procedure based on SC goals Heckmann et al (2015), in accordance to Borgström (2005), defined efficiency as "a way to attain the SC’s goals through taking minimal resources and thereby achieving the cost-related advantages." Further, they defined effectiveness as "obtaining pre-determined SC goals even in the face of inverse conditions or unexpected events." In SCND, most studies have assumed a single objective function for their optimization models, which usually seeks to achieve eco- K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 127 Table Solution approach and specifications of the mathematical model for scenario-based robust problems Articles Solution approach Exact algorithm Heuristic Meta-heuristic Realff et al (2004) AIMMS Aghezzaf (2005) [1] Pan and Nagi (2010) LR algorithm A heuristic based on k-shortest path algorithm Kara and Onut (2010b) Peng et al (2011) De Rosa et al (2013) Ramezani et al (2013b) Tian and Yue (2014) CPLEX CPLEX CPLEX SA [2] Exact algorithms: 6%, Heuristic algorithms: 12%, Meta-heuristics: 18%, Commercial solvers: 64% Min(Max(Regret(I-C1-C2-C3-C4C16))) Min M1 +M2 Min(C1+C3+C4 +C6+C12 +C14), Min M MILP-TSSP MILP-TSSP MILP-TSSP MILP-TSSP LINGO MILP-TSSP MINLP-TSSP CPLEX MILP MILP-TSSP CPLEX CPLEX MILP MILP CPLEX MILP-TSSP artificial fish swarm algorithm Govindan and Fattahi (2017) Table’s summary: MILP-TSSP MILP-TSSP TS Hatefi and Jolai (2014) Li et al (2015) Objective MILP-TSSP Benders’ decomposition Jabbarzadeh et al (2014) Jin et al (2014) Mathematical model MILP-TSSP MILP-TSSP GA Ahmadi-Javid and Seddighi (2013) Torabi et al (2016) Sadghiani et al (2015) Commercial solver MILP: 92%, MINLP: 6% Max(I-C1-C4-C16-C18), Min M Min(C1+C4) Min M Min(Max(Regret(I-C1-C4-C5-C6C7-C16))) Min(Max(C1 +C17+(production and distribution disruption costs))) Min(C1+C4+C5+C6+C7 +C8+C10+C14) Min(C1+C3+C4+C6), Min M Min(C1+C4+C5+C6+C8), Min M Min(C1+C4+C5+C6+C14+C16) Min(C1+C4+C6+C12+C14) Min(C1+C4+C5+C6+C14+C16) Min(C1+Capital costs of transportation modes), Min M1 , Min M2 Min(Max(C1+C3+C4+C5 +C6+C7+C14)) Single objective (Minimization: 60%, Maximization: %), Multiple objectives: 40% [1], [2], These papers considered two robustness measures including solution’s and model’s robustness measures to less conservative solutions through allowing the uncertainty sets to be ellipsoids Nonetheless, their robust formulations resulted in nonlinear but convex models, and thereby being difficult to solve as compared to Soyster’s method Bertsimas and Sim (20 03, 20 04) presented a different robust approach in which the conservatism level of robust solutions could be controlled and resulted in a linear optimization model This approach is also applied for discrete optimization models However, Ben-Tal, Goryashko, Guslitzer, and Nemirovski (2004) pointed out that in all above conventional RO approaches, all decisions have to be made before uncertainty realization Nevertheless, most real-world problems, in particular SCND problem, have multi-stage nature, and hence some decisions have to be determined after realization of all or part of existing uncertainties To this aim, they presented a multi-stage RO approach, called Affinely Adjustable Robust Counterpart (AARC) This idea allows for making adjustable decisions that are affinely contingent on the primitive uncertainties In practice, even though the exact distributions of uncertain parameters are often not known in advance, moment information or uncertainty about the distribution itself is usually known To deal with this situation, Distributionally Robust Optimization (DRO) was firstly proposed by Scarf, Arrow, and Karlin (1958) and then extended by Delage and Ye (2010), Goh and Sim (2010), and Wiesemann, Kuhn, and Sim (2014) In DRO, an uncertain parameter follows a distribution which is itself subject to uncertainty In the area of SCND problem, a few studies proposed robust counterpart formulations where interval-uncertain parameters are taken into account In Table 10, these studies are listed in which robust problems are solved after proposing their equivalent tractable formulations The specifications of these equivalent formulations are also highlighted in Table 10 As illustrated in Table 10, there are a few studies about robust SCND with interval-uncertainty Most of these reference papers used commercial solvers to solve the equivalent models for their robust counterparts It is worth noting that in Keyvanshokooh et al (2016) and Hatefi and Jolai (2014), some uncertain parameters have interval-uncertainty and some others are modeled by using discrete scenarios This approach is applicable whenever we have different types of uncertainty in the SCND problem 5.7 Fuzzy mathematical programming in the context of SCND Fuzzy mathematical programs have been commonly used to design SC networks under uncertainty In general, the fuzzy mathematical programming can be divided into flexible and possiblistic programming Consider the classical linear program Min cT x, s.t Ax ≥ b, x ≥ In accordance with Tanaka, Okuda, and Asai (1973) and Zimmermann (1991), a flexible pro cT x, s.t Ax≥b, ˜ gramming problem can be written as Min x≥0 where fuzzy goals and sets are utilized to characterize the vagueness related to decision maker’s aspirations and constraints, respectively In other words, this approach is applicable to deal with flexible target value of goals and elasticity of soft constraints On the other hand, a possiblistic programming problem can  c˜T x, s.t A˜ x ≥ b˜ , x ≥ where the imprecise or be expressed as Min ambiguous data is modeled through possibility distributions (see Tanaka & Asai, 1984) The application of this approach is to manage deficiency of information for the exact values of a model’s parameters Moreover, in fuzzy mathematical programming, it is possible to take care of ambiguous coefficients and also vague preferences of decision makers All studies in this area have two major phases to solve a problem modeled using a fuzzy mathematical programming Firstly, 128 K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 Table 10 Solution approach and specifications of the equivalent formulations for robust counterpart of RO problems Articles Solution approach Exact algorithm Equivalent model for robust counterpart of problems Heuristic Meta-heuristic Commercial solver Mathematical model Pishvaee, Rabbani, and Torabi (2011) Hasani, Zegordi, and Nikbakhsh (2012) Vahdani et al (2012) CPLEX MILP Min(C1+C4+C14) LINGO MINLP GAMS MILP Zokaee, Jabbarzadeh, Fahimnia, and Sadjadi (2014) Hatefi and Jolai (2014) Tong, You, and Rong (2014) LINGO MILP Max(I-C1-C3-C4-C5-C8-C10C14-C16) Min(C1+C4+C5+C6+C16), Min(Disruption cost) Min(C1+C4+C14) CPLEX DICOPT, BARON, SBB MILP MINLP Min(C1+C4+C5+C6+C14+C16) Min((C1+C4 +C5+C6+C7+C11Governmental incentives)/ Sales’ amount) MINLP Max(I-C2-C3-C4-C5-C8-C10C15-C16) Parametric approach based on Newton’s method, Reformulationlinearization method Hasani et al (2015) Combined memetic algorithm and adaptive VNS Akbari and Karimi (2015) Dubey, Gunasekaran, and Childe (2015) Keyvanshokooh et al (2016) CPLEX CPLEX Benders’ decomposition Hasani and Khosrojerdi (2016) Table’s summary: MILP Memetic algorithm Exact algorithms: 9%, Heuristic algorithms: 9%, Meta-heuristics: 18%, Commercial solvers: 64% MILP MILP MILP: 72%, MINLP: 28% a fuzzy model is converted into a crisp and usual mathematical model in which the existing uncertainties are handled according to assorted interpretation of the problem Then in the second phase, this transformed mathematical model is solved by using an optimization approach or tool (Inuiguchi & Ramık, 20 0) SCND problems under a fuzzy environment are categorized in Table 11 based on their fuzzy uncertainties, transformed mathematical models, and solution approaches It should be noted that in Table 11, we report the optimization tools or techniques for solving the crisp transformed mathematical models as solution approaches Here, the techniques used for handling multi-objective problems or transforming fuzzy models are not considered In Table 11, in the column for mathematical model, the dashes mean that no crisp transformed model is presented in related studies As shown by Table 11, most studies in this area considered ambiguous input data to present a possiblistic programming model and used commercial solvers to solve the transformed equivalent crisp models Moreover, many studies dealt with multi-objective problems in this area 5.8 Optimization approaches for SCND with disruptions As SCND with disruptions has received much attention recently, we discuss different optimization approaches to cope with this problem in this section Lately, Snyder et al (2016) provided a review paper regarding the management science and operation research models for handling SC disruptions Further, Laporte et al (2015) examined the existing FL models under disaster events SCND studies with disruptions can be divided into business and non-business SCs The goal of a business one is to design a SC such that it can perform well even after disruption occurrence The nonbusiness SCs such as Liu and Guo (2014), Noyan (2012), and Jeong et al (2014) are often designed to deliver relief items to the es- MINLP Objective Min(C1+C3+C4 +C5+C6+C7) Min(C1 +C4+C5+C6+C7+C16), Min(Delivery time + Collection time) Max(I-C1-C3-C4-C5-C7-C14C16) Max(I-C2-C3-C4-C5-C8-C10C15) Single objective (Minimization: 46%, Maximization: 36%), Multiple objectives: 18% tablished demand points after disasters and is called humanitarian SC While SC disruptions can have substantial influence on key SC parameters such as demand, supply, delivery time of products, and costs, they may also result in reducing capacity of SC facilities and transportation links or even eliminating them In addition, in humanitarian SCs, the demand for relief supplies has a great deal of uncertainty, depending on the type, magnitude, and location of a disaster In this area, most studies assume a failure probability for a facility or transportation link in the face of disruption as a pre-specified parameter They are also called reliable SCND models These studies include Azad et al (2014), Azad, Saharidis, Davoudpour, Malekly, and Yektamaram (2013), Cui et al (2010), Hatefi, Jolai, Torabi, and Tavakkoli-Moghaddam (2015a), Li and Savachkin (2016), Li, Zeng, and Savachkin (2013), Marufuzzaman, Eksioglu, Li, and Wang (2014), Vahdani et al (2012), Vahdani, Tavakkoli-Moghaddam, Jolai, and Baboli (2013), Vahdani, Tavakkoli-Moghaddam, and Jolai (2013), and Hatefi, Jolai, Torabi, and Tavakkoli-Moghaddam (2015b) In Cui et al (2010), customers are assigned to more than one facility and hence in the face of disruption, each customer can be served by the nearest operational (non-disrupted) facility Azad et al (2014) presumed that if a failure occurs for a facility of SC, then the percentage of its disrupted capacity is a stochastic parameter They also presented an optimization model by using the CVaR measure Sometimes, the uncertainty related to disruptions is modeled as a finite set of discrete scenarios In this regard, Hatefi and Jolai (2014), Peng et al (2011), and Li et al (2015) utilized the p-robustness approach Also, Ahmadi-Javid and Seddighi (2013), Noyan (2012), Sadghiani et al (2015), and Baghalian, Rezapour, and Farahani (2013) developed some risk-averse scenario-based stochastic models by using well-known risk measures in the stochastic programming context It is worth noting that most SCND K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 129 Table 11 Optimization aspects related to the studies under fuzzy environment Articles Fuzzy mathematical programming Xu, Liu, and Wang (2008) Selim and Ozkarahan (2008) Xu, He, and Gen (2009) Pishvaee and Torabi (2010) Qin and Ji (2010) [1] Zarandi, Sisakht, and Davari (2011) Pishvaee, Torabi et al (2012) Pishvaee and Razmi (2012) Pishvaee, Razmi, and Torabi (2012) Vahdani et al (2012) Bouzembrak, Allaoui, Goncalves, Bouchriha, and Baklouti (2013) Vahdani, Tavakkoli-Moghaddam, and Jolai (2013) Vahdani, Tavakkoli-Moghaddam, Jolai, and Baboli (2013) Jouzdani, Sadjadi, and Fathian (2013) Mirakhorli (2014) Ambiguous data √ Ramezani, Kimiagari, Karimi, and Hejazi (2014) Pishvaee et al (2014) Bai and Liu (2016) Özceylan and Paksoy (2014) √ √ Tong, Gleeson, Rong, and You (2014) Sadjadi, Soltani, and Eskandarpour (2014)[2] Mousazadeh et al (2015) Torabi et al (2016) Hatefi et al (2015a) Hatefi et al (2015b) Fallah, Eskandari, and Pishvaee (2015) Sadghiani et al (2015) Babazadeh et al (2017)[3] Table’s summary: Mathematical model Solution approach MINLP Spanning tree based GA CPLEX Spanning tree based GA LINGO MILP MILP MILP √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ Exact algorithms: 3%, Heuristic algorithms: 0%, Meta-heuristics: 18%, Commercial solvers: 79% Min(C1+C4+C14), Max R Min(C2+C4), Min(C1), Max R Min(C1+C4) Min(C1+C4+C5+C6+C16), Min (Delivery tardiness) Min(C1+C4+C16+C18) MILP MILP MILP MILP LINGO LINGO LINGO Min(C1+C4+C5+C7+C11), Min E Min(C1+C4+C5+C16), Min E Min(C1 +C4+C5+C11), Max S MILP GAMS MILP CPLEX Min(C1+C4+C5+C6+C16), Min(Disruption cost) Min(C1+C3+C4+C6) MILP GAMS MILP GAMS MINLP LINGO MILP GA MILP CPLEX MILP MILP LINGO Imperialist competitive algorithm (ICA) CPLEX MILP √ √ Objective GA integrated with fuzzy simulation CPLEX MILP √ Subulan, Tas¸ an, and Baykasog˘ lu (2014) Subulan, Baykasog˘ lu et al (2014) Crisp transformed mathematical model Vagueness of goals √ Balaman and Selim (2014) Jindal and Sangwan (2014) Vahdani, Dehbari, Naderi-Beni, and Kh (2014) Vagueness of constraints MILP MINLP Benders’ decomposition LINGO GAMS MILP CPLEX MILP CPLEX MILP CPLEX MILP Memetic algorithm CPLEX MILP MILP CPLEX CPLEX MILP CPLEX MINLP GAMS MILP CPLEX MINLP[1] CPLEX MILP: 88%, MINLP: 12% Min(C1 +C7+C4), Max R Min(C1+C4+C5+C6+C16), Min(Disruption cost) Min(C1+C4+C5+C6+C16), Min(Disruption cost) Min(C1+Traffic congestion cost) Min(C1+C4+C5+C6+C16), Min (Service time) Min(I-C1-C2-C4-C6-C7-C8), Min (Unused waste) Max(I–C1-C4-C8-C16) Min(C1+C4), Max(Reliability of facilities) Max(I-C1-C3-C4-C5-C6-C8-C10C16), Max R Min(C1+C4+C5+C6+C7+C11 +C16-C19), Min E, Max S Min(C1+C4+C5+C8) Min(C1), Min(C4), Min(C8), Min(C16) Min(C1+C4+C5+C8+C16-I), Max (Coverage of return products), Max (flexibility) Min(C1+C4+C5+C8+C16-I), Max (Coverage of return products) Min(C1 +C3+C4 +C5+C6+C7+C11-Government incentives) Min(C1+C2+C4), Min (Variance of constrains’ deviations) Min(C1+C3+C4+C5+C7+C11), Min(Max(unsatisfied demand)) Min(C1+C4+C5+C6+C14+C16) Min (C1+C4+C5+C6+C16 +Disruption cost) Min (C1+C4+C5+C6 +C16+Disruption cost) Max(I-C4-C5-C16) Min(C1+Capital costs for transportation modes), Min M1 , Min M2 Min(C1+C3 +C4 +C5+C6+C7+Importing cost), Min E Single objective (Minimization: 27%, Maximization: %), Multiple objectives: 67% [1], [2], The crisp transformed model is not presented in these studies [3]In this study, the MINLP model is transferred to an MILP one 130 K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 models with disruptions in the literature are single period and only a few papers such as Klibi and Martel (2012a) and Klibi and Martel (2013) can be found which are multi-period Survey papers by Tang (2006a), Tang (2006b), Tang and Tomlin (2008), and Tang and Musa (2011) introduced mitigation strategies which could be utilized to improve SC’s resiliency in the face of risks Moreover, some mitigation strategies expressed by Tang (2006a) and Tang and Tomlin (2008) can be applicable for dealing with operational risks in SCs, which reveals the fact that they are not developed only for disruption risks However, in SCND, these strategies have been applied to handle a SC under the uncertainty induced by disruptions Further, a few papers employed mitigation strategies for designing a resilient SC network Here, we explore the most popular mitigation strategies in the related literature: Facility fortification: In this strategy, some facilities are chosen for an existing SC network or during the design phase of a SC network in order to fortify them against various disruptions Hasani and Khosrojerdi (2016), Li and Savachkin (2016), and Qin, Liu, and Tang (2013) utilized this strategy Strategic stock: Using this strategy, a SC can hold the inventory for raw materials, semi-finished and finished products in its facilities within different layers of SC This inventory is often utilized to satisfy the needs of customers and other manufacturing processes Benyoucef, Xie, and Tanonkou (2013), Hasani and Khosrojerdi (2016), Mak and Shen (2012), Qi and Shen (2007), and Qi, Shen, and Snyder (2010) employed this strategy Sourcing strategy: As pointed out by Snyder et al (2016), this strategy is divided into multiple sourcing and backup sourcing In the multiple one, sourcing is carried out by using multiple suppliers simultaneously before disruption occurrence However, the backup sourcing exploits backup suppliers when primary suppliers are disrupted Cui et al (2010), Hasani and Khosrojerdi (2016), Klibi and Martel (2012a), Klibi and Martel (2013), Mak and Shen (2012), Qi and Shen (2007), and Li et al (2013) used one or both strategies Applications and real-word case studies for SCND Here, some studies that deal with applications of SCND problem under uncertainty have been reviewed In this regard, some of them investigated real-life case studies and some others solved randomly generated test instances in an industrial context One of the essential challenges in designing a SC network based on a specific industrial context is that the design decisions have to be often made according to required processes for producing products (e.g., Schütz et al (2009) and Govindan and Fattahi (2017) that studied a SC for a meat and glass industry, respectively) In a survey paper by Barbosa-Povoa (2014), SCs formed for process industries, named as process SCs, are examined For this aim, the real-life case studies are divided into five major types, including agricultural, biomass/biofuel, gas/hydrogen, pharmaceutical, and oil SCs Unlike studies related to business SCs, non-business SC models are often developed based on a specified application In Table 12, the reference papers developed for specific application or industry and the ones that examined some real-world case studies are listed In the column for real-life case study, the dashes mean that the related reference paper did not examine a real-life case study and solved some randomly generated test instances for the considered industry or application As shown in Table 12, about 24% of reference papers defined their SC networks on the basis of a specific industry or applica- tion It is worthwhile to focus more on designing SC networks for specific industries in business SCs and applications in non-business SCs Moreover, due to difficulties in collecting, preparation, and aggregation huge data sets, only 20% of reference papers concerned real-life case studies In this regard, big data analytics tools and techniques would be helpful for future research works In terms of the type of logistics networks, about 20% of papers treated the applications of RL or CLSC networks in Table 12 Here, the biomass/biofuel, chemical, gas/hydrogen, and pharmaceutical SCs include 28%, 10%, 10%, and 5% of studies, respectively Thus, it can be concluded that researchers have paid more attention to biofuel/biomass SCs recently Furthermore, a review and systematic classification on biomass to energy SC networks is presented by Balaman and Selim (2015) Discussion, conclusions, and future research directions In this paper, a comprehensive review was presented on the studies in the area of SCND problem under uncertainty The decision-making environments under uncertainty were divided into three categories in Section In general, the uncertainty sources include (1) the existing uncertainty in parameters such as supply, demand, and costs, which are inherently uncertain, and (2) the uncertainty caused by natural or man-made disruptions Fewer than 20% of studies considered the second uncertainty source in their problems Therefore, addressing reliable and resilient SC networks under disruption risks will have high potential as a future research direction In this paper, we answered the questions mentioned in the introduction section For this aim, the studies were investigated from two principal perspectives involving (1) SCM aspects, and (2) optimization aspects In this section, a discussion is presented and several future research directions on the basis of literature’s gaps are provided from these two perspectives, separately 7.1 SCM aspects in SCND under uncertainty The integration of strategic SC decisions and the other ones related to tactical/operational levels in a comprehensive model under uncertainty will be a future research direction More specifically, a few reference papers coped with decisions such as routing and price of products Pricing of products and revenue management issues are addressed by some studies (e.g., Ahmadi-Javid & Hoseinpour, 2015; Fattahi et al., 2015) for deterministic problems, and these studies have the potential to be extended for an uncertain environment Moreover, a small number of papers have dealt with vehicle routing decisions in a SCND problem under uncertainty, all of which considered routing decisions only for one layer of SC network Hence, this area requires more attention in the sense that we may make routing decisions for more than one layer of SC or consider the vehicles with different types and capacities Further, as pointed out in Section 4.2, many studies made inventory and design decisions simultaneously for single or multiple layers of a SC network However, making such decisions for SCs with highly perishable products such as blood SCs often depends on the products’ characteristics and life cycle There has not been any study that handles this aspect in SCND under uncertainty and hence it promises to be an interesting future research topic Only 32% of reference papers took a planning horizon with multiple periods into account Due to the strategic nature of SCND decisions, defining strategic periods will help a decision maker to have the opportunity of changing strategic decisions in future with respect to the volatile business environment Additionally, tactical or operational periods can capture changes in the parameters associated with these decision levels Thus, developing comprehen- K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 131 Table 12 Applications and industrial contexts addressed in the related literature Articles Non-business supply chain Realff et al (2004) Listes¸ and Dekker (2005) Guillen et al (2006) You and Grossmann (2008a) Rappold and Van Roo (2009) Guillén-Gosálbez and Grossmann (2009) Schütz et al (2009) Guillén-Gosálbez and Grossmann (2010) Lee et al (2010) Sabio et al (2010) Kim et al (2011) Giarola et al (2012) Noyan (2012) √ Chen and Fan (2012) Almansoori and Shah (2012) Gebreslassie et al (2012) Kazemzadeh and Hu (2013) Baghalian et al (2013) Jouzdani et al (2013) Tong et al (2013) Balaman and Selim (2014) Jeong et al (2014) √ Marufuzzaman et al (2014) Jabbarzadeh et al (2014) √ Zokaee et al (2014) Tong, You et al (2014) and Tong, Gleeson et al (2014) Madadi et al (2014) Li and Hu (2014) Liu and Guo (2014) Pishvaee et al (2014) Subulan, Tas¸ an et al (2014) and Subulan, Baykasog˘ lu et al (2014) Dayhim et al (2014) Ayvaz et al (2015) Hasani et al (2015) and Hasani and Khosrojerdi (2016) Mousazadeh et al (2015) Babazadeh et al (2017) Govindan and Fattahi (2017) √ A specific industry or application Recovery network for carpet recycling Recovery network for recycling sand A supply chain for chemical industry A supply chain for polystyrene industry A supply chain for handling reparable items A supply chain for chemical industry A supply chain for meat industry A supply chain for chemical industry A supply chain for an international electrical company Hydrogen supply chain Biofuel supply chain Ethanol supply chain A supply chain network for distributing relieif supplies after occurrence of a disaster Bioethanol supply chain Hydrogen supply chain Hydrocarbon biorefinery supply chain Biofuel supply chain A supply chain for an agri-food industry Milk and dairy supply chain Hydro carbon biofuel and petroleum supply chain Bioenergy supply chain A supply chain network for distributing relieif supplies after occurrence of a disaster Biofuel supply chain A supply chain network for blood distribution after occurrence of a disaster Bread supply chain Hydro carbon biofuel supply chain Real-life case study A A – – – A A A A case study in USA case study in Netherlands case case case case study study study study in in in in Europe Norway Europe Asia Pasific region A case study in Spain A case study in southern part of USA – – A case study in the state of California (USA) A case study in Great Britain A case study in the state of Illinois (USA) A case study in the state of Iowa (USA) The rice industry of a country in the Middle East A case study in Iran – A case study in Turkey A case study in the state of South Carolina (USA) based on historical disasters A case study in the southeast region of USA A case study for Tehran’s earthquake A case study in Iran A case study in the state of Illinois (USA) Pharmaceutical supply chain Biofuel supply chain A supply chain network for distributing relieif supplies after occurrence of a disaster A CLSC for medical needle and syringe industry A CLSC for lead/acid battery industry – A case study in the state of Iowa (USA) A case study based on Great Wenchuan earthquake in China A case study for an industry in Iran A case study for an industry in Turkey Hydrogen supply chain RL for waste management of electrical and electronic equipments A CLSC for medical devices industry A case study in the state of New Jersey (USA) A case study in Turkey A case study in Iran Pharmaceutical supply chain Biodiesel supply chain A supply chain for glass industry A case study in Iran A case study in Iran A case study in Iran sive models under uncertainty with multiple periods requires more attention In particular, deterministic multi-period SCND problems in which there exists the possibility of changing the location and capacity of facilities over different strategic periods, have been widely addressed (e.g., Melo et al., 2006; Thanh, Bostel, & Péton, 2008) These studies also have potential to be extended for an uncertain decision-making environment Moreover, we could not find any SCND study under uncertainty that deals with a planning horizon where strategic and tactical periods are integrated As shown by Fig 9, a few papers addressed social responsibility or environmental aspects in designing SC networks under uncertainty Nevertheless, government legislation and customers’ awareness have caused most corporations and organizations to pay more attention to these issues Evidently, more research is still required on these aspects, whose significances have been emphasized and raised by social and environmental concerns Further, dealing with financial factors and different types of competitions in SCND problems under uncertainty are another two potential research areas Farahani et al (2014) surveyed competitive SCND and represented the existing research gaps in this area Designing humanitarian SC networks needs more investigations, and indeed many studies in this area can be done with respect to different disaster types and desired applications Sometimes, it may not be possible to satisfy all demands in humanitarian SC networks, so there is a need to develop models considering fairness for shortages that may occur at different demand points Moreover, demand points in this type of network often need different commodities, but their priority varies This aspect has been rarely regarded in humanitarian SC networks In general, two aspects that should be considered by researchers in this area are: (1) planning decisions, network structure and performance measures depend on the considered application and can be quite different from business SCs; and (2) modeling uncertain parameters is contingent upon the type and magnitude of disasters Designing responsive SC networks has been examined by only 12% of reference papers In these studies, the fill rate of customers’ demands and their service time are often used as performance measures for evaluating the responsiveness of SC In all of these studies, customers’ demand is not dependent on the responsiveness of SC Nonetheless, in today’s competitive business environ- 132 K Govindan et al / European Journal of Operational Research 263 (2017) 108–141 ment, designing a SC network in which customers’ demand is sensitive to SC’s responsiveness is a valuable future research Moreover, defining other criteria for the SC’s responsiveness based on business goals of companies is of importance in different applications Finally, there were a few papers to cope with real-world situations The reason is twofold: (1) the necessity for collecting a large data set to model comprehensive SCND problems, and (2) the difficulties in obtaining correct estimates for uncertain parameters Thus, it would be worthwhile to carry out studies based on a SC network defined for real-life case studies 7.2 Optimization aspects in SCND under uncertainty In this paper, assorted modeling frameworks that have been applied for SCND problems under uncertainty were introduced and thus the studies were investigated in terms of their developed solution methodologies and mathematical models In this section, research gaps and potential future research guidelines in terms of optimization aspects are discussed More than 50% of reference papers made use of commercial solvers to solve their optimization problems This fact demonstrates two practical issues Firstly, commercial solvers have had significant progress over recent years such that they have suitable performance in solving optimization problems in this area Second, many industries would prefer to exploit a proven commercial solver for solving smaller problem instances instead of using a custom designed solution approach, which results in an approximate solution A few studies applied meta-heuristics approaches Due to the NP-hardness nature of SCND problem under uncertainty, developing this type of solution approaches still remains a future research direction It is worth noting that meta-heuristics cannot guarantee the optimal solution for an optimization problem However, these approaches can solve large-scale problems within appropriate time Therefore, developing this kind of solution approaches is worthwhile Further, presenting solution algorithms, which are based on the combination of exact methods with heuristics or meta-heuristics is another future area of research In scenario-based stochastic programs for SCND, Benders’ decomposition or L-shaped method, as exact approaches, were widely applied due to the problem’s special structure However, exact solution approaches for problems with minimax or weighted mean-risk objectives are still scarce and will be welcomed by researchers and practitioners In addition, developing multi-stage stochastic programs and presenting efficient solution approaches for them is another challenging issue, and it needs greater consideration In this regard, the progressive hedging algorithm, an applicable method for solving two and multi-stage stochastic programs, has been used scarcely in the related literature Another significant aspect for scenario-based stochastic programs is to generate an efficient set of scenarios to model underlying stochasticity in SCND More importantly, evaluating scenario generation methods in terms of stability and quality criteria should be examined in SCND problem as well There are different approaches to deal with scenario generation and reduction in the Stochastic Programming community (e.g., Dupacˇ ová et al., 2003; Heitsch & Römisch, 20 03; Høyland & Wallace, 20 01) that can be applied in this research area As mentioned before, there exist two types of risks including operational and disruption risks in a SC, for which risk management plays an indispensable role in reducing these existing risks Because only a few papers addressed this issue, risk management in SCND problem is a potential future research direction By exploring the papers in Section 5.5, it can also be highlighted that most ones utilized the well-known risk measures for alleviating the risks based on their economic objectives such as SC’s cost or profit However, studying the SC’s risk based on other strategic goals of SC such as responsiveness is still a challenge It is worth noting that Heckmann et al (2015) discussed this research gap in the area of supply chain risk management with more details Moreover, most SCND models with disruption risks are single period in the related literature However, disruptions can affect the SC’s performance for a long time Thus, developing SCND models under a planning horizon with multiple periods and modeling uncertain effects of disruptions over this planning horizon is another concern Further, a number of papers employed some mitigation strategies for managing SC’s disruption risks, as discussed in Section 5.8 However, as pointed out by Tang (2006a) and Tang and Tomlin (2008), there are other mitigation strategies such as flexible manufacturing process, responsive pricing, supply contracts, and so on that can be used for designing resilient SCs Hence, future research works may develop SCND models based on these other strategies and assess their effectiveness It is worth mentioning that using mitigation and contingency strategies simultaneously is another interesting future research for designing resilient SC networks Robust SCND has gained less attention in comparison with fuzzy and stochastic programs However, it must be noted that in many real-world applications, enough historical data are not present to estimate parameters’ distributions, but robust optimization is a suitable tool for handling such a situation Using AARC and DRO approaches in the area of SCND problems is another research direction for which there has not been any paper in the related literature Additionally, developing modeling approaches in the context of SCND problem that fill out the gap between stochastic programming and RO could be an interesting research idea In addition to these aspects, exploring new applicable robustness measures to address solution or model robustness will be another promising research direction Simulation is a powerful tool to validate obtained policies in uncertain decision-making environments and unfortunately, such a methodology has been rarely examined in the related SCND literature In addition, to the best of our knowledge, there has not been any research to compare different modeling philosophies such as stochastic programming, RO, and fuzzy programming to design a SC network under uncertainty Therefore, a systematic comparison between these modeling approaches will be required The last conclusion that can be drawn from this survey paper is while there are many research studies for SCND problem under uncertainty, this research area still needs more studies presenting realism models based on real-world applications and handling computational aspects to solve large-sized problems Acknowledgment The authors would like to thank the editor and the anonymous reviewers for their invaluable comments which improved this paper significantly ... 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